The enhancement in the curvature power spectrum not only seeds the primordial blackholes, but it may also act as a source for the tensor perturbations at the nonlinear order, producing scalar-induced second-order gravitational waves [1]}, [2]}, [3]}, [4]}.
Therefore, inflation models in which primordial blackholes are formed via large enhancement of the curvature perturbation inevitably produce the scalar-induced second-order gravitational waves.
Detection or non-detection of gravitational wave signals may thus confirm or constrain the mass ranges of the primordial blackholes.
For example, from the pulsar timing array experiments, a relatively large mass range of \([0.1M_{\odot },10M_{\odot }]\)  (\(M_{\odot }\)  is the solar mass) is strongly constrained [5]}, [6]}.
Recently, the NANOGrav Collaboration reported a hint for stochastic gravitational wave signals [7]}.
In Refs. [8]}, [9]}, [10]}, [11]}, [12]} the connection between the NANOGrav results and the primordial blackholes is investigated.
The future gravitational wave experiments such as LISA [13]}, [14]}, DECIGO [15]}, [16]}, and BBO [17]}, [18]}, [19]}, may probe smaller mass ranges of primordial blackholes.
Other recent studies on the primordial blackholes and the scalar-induced second-order gravitational waves include Refs. [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}, [31]}, [32]}, [33]}, [34]}, [35]}, [36]}.
